Question

The base and height of a ∆ are in the ratio 3:2 and it's area is 108cm? Find it's base and height.

Answer 1

The ratio of base and height of a Δ = 3:2
Let us assume that base = 3x cm and height = 2x cm
Given area of the Δ = 108 cm²
⇒1/2 ×3x × 2x = 108
⇒1/2 × 6x² = 108
⇒ 6x² /2 = 108
⇒ 3x² = 108
⇒  x² = 108/3
⇒  x² = 36
⇒  x = √36  or   x = -√36
⇒ x = 6   or  x = -6
∵ dimensions can not be negative x = 6
∴Base = 3x = 3(6) = 18 cm
Height = 2x = 2(6) = 12 cm

Answer 2

Let the base and height of the triangle be 3x and 2x respectively.
1/2 x 3x x 2x = 108
1 x 3x x x = 108
3x^2 = 108
x^2 = 36
x = 6
Base = 18
Height = 6